Pluripotent stem cells (PSCs) proliferate over long periods and can differentiate to many cell types of the body. Since they can be derived from humans (hPSCs) and indeed from any healthy individual or patient, they are becoming an increasingly important source of human cells for tissue engineering, modelling human disease, drug discovery and safety pharmacology. Efficient directed differentiation of hPSCs toward both vascular endothelial cells (ECs) and the adjacent mural cells (pericytes or mesenchymal stromal cells (MSCs) and vascular smooth muscle cells (vSMCs)) that provide vessels with stability, is however crucial for all of the above applications. Moreover, vascular differentiation of hPSCs could reveal early-unknown steps in endothelial specification during human development, and lead to better understanding of mechanisms that cause vascular defects and underlie different cardiovascular diseases. Understanding the underlying molecular signals driving differentiation and their timing is therefore important in a much broader context.